Basic Electricity And Electronics

Citation preview

V.S. Popov, S.A. Nikolayev

Basic Electricity and Electronics

Mir Publishers Moscow

B. C. rionoB, C. A. HMKo/iaeB OBLUAfl 3/1EKTPOTEXHHKA C OCHOBAMkl 3J1EKTPOHMKM SHeprHfl MocKBa 1977

V. S. Popov

Basic

and

Electricity

S. A. Nikolaev

and Electronics

Translated from the Russian l>y Alexander Kuznetsov

M ir Publishers • Moscow

First published 1979 Revised from the 1977 Russian édition

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The Greek Alphabet Aa BP Ty

Aô E8 H t, e^e

Alpha Beta Gamma Delta Epsilon Zêta Eta Thêta

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© H3flaTejibCTB0 «3HeprnH», 1977 © English translation, Mir Publishers, 1979

Rho Sigma Tau Upsilon Phi Chi Psi Oméga

Contents

Introduction

15

PART ONE. ELEC TR IC ITY .................................

17

Chapter One. Electric F i e l d ......................................................

17

1-1. G e n e ra l.............................................................................. 1-2. Voltage. P o t e n t i a l .......................................................... 1-3. Electric Conduction ...................................................... 1-4. Capacitance. Capacitors ............................................... 1-5. Connection of Capacitors . . .................................... 1-6. Energy of the Electric F i e l d ....................................... 1-7. Polarization of D ie le c tric s ........................................... 1- 8. Electric Insulating M a te r ia ls .................... , . . . .

17 19 20 23 26 28 29 31

Chapter Two. Direct-Current Circuits

.......................................

2-1. Electric Current .......................................................... 37 2-2. Electric Circuit and Its C o m p o n en ts............. 2-3. Ohm’s Law .................................................................. 2-4. Electric Résistance and C o n d u ctan c e............. 41 2-5. Relationship between Résistance and Température 2-6. Conductor Materials .................................................. 2-7. Energy and P o w e r ...................................................... 2-8. Conversion of Electric Energy into H e a t ..... 49 2-9. Electric Load on Wires and Overload Protection 2- 10. Voltage Loss in W i r e s ..................................... 52 2-11. Kirchhoff’s First (Current) L a w ..................... 53 2-12. Sériés Combination of Résistances (Loads) . . . . 2-13. Parallel Combination of Résistances (Loads) . . . 2-14. Series-Parallel Combination of Résistances (Loads) 2-15. Two Modes of Operation of Power Source . . . . 62 2-16. Kirchhoff’s Second (Voltage) L a w ................. 2-17. Solution of Complex Circuits ...................................

35 35 40 44 46 47 50 54 55 58 59 63

6

Contents 2-18. Chemical Sources of Current ................................... (a) Primary Cells ....................................................... (b) Storage Cells (Secondary Chemical Sources of Current) .................................................................. 2-19. Combinations of Chemical Current Sources . . . . 2- 20. Nonlinear Circuits ...................................................

Chapter Three. Electromagnetism

65 65 67 71 73 77

3-1. 3-2. 3-3. 3-4. 3-5.

Magnetic Field of a C u r r e n t ....................................... 77 Magnetomotive Force, Magnetic Field Strength . . 80 Ampere’s Circuital L a w ............................................... 82 Magnetic Induction, Permeability, Magnetic Flux 83 Electromagnetic Force ............................................... 86 (a) A Straight Current-Carrying Wire in a Magnetic 86 F i e l d .......................................................................... (b) A Current-Carrying Loop in a Magnetic Field . . 89 (c) An Electron Moving in a Magnetic Field . . . . 89 3-6. Interaction of Parallel Current-CarryingConductors 90 3-7. The Magnetic Field due to a Current-Carrying Coil 91 3-8. Ferromagnetics. Magnetization and Reversai of M agnetization.................................................................. 93 3- 9. Ferromagnetic Materials ......................................... 97 (a) Soft Magnetic Materials ................................... 97 (b) Hard Magnetic Materials ................................... 99 3- 10. The Magnetic Circuit and Its D e s ig n in g ............ 100 3-11. E lectrom agnets............................................................... 102 104 3-12. Electromagnetic Induction ....................................... 104 (a) The EMF Induced in a C o n d u c to r... (b) The EMF Induced in a Loop ....................... 105 3-13. Operating Principle of an Electric Generator . . 108 109 3-14. Operating Principle of an Electric M o t o r ............... 3-15. Eddy C u r r e n ts .............................................................. 111 3-16. Inductance. EMF of Self-Induction ........................ 113 3-17. Energy of the Magnetic F i e l d ................................... 115 3-18. Mutual I n d u c ta n c e ....................................................... 116 3- 19. Magnetohydrodynamic Generator ........................ 118 Chapter Four. Direct-Current Electric M a c h in e s .................... 4- 1. F unctions...................................................................... 4-2. Design of D. C. M a c h in e s ........................................... 4-3. Operating Principle of a D. C. M a c h in e .................... 4-4. Construction of the Armature W i n d i n g .................... 4-5. The EMF of the Armature W i n d i n g ........................ 4-6. The Electromagnetic Torque of a M a c h in e ................ 4-7. Mechanical Power of a D. C. M a c h in e ........................ 4-8. Armature Reaction of a D. C. Machine ................ 4-9. C om m utation.................................................................. 4- 10. Ratings and Characteristics of Electric Machines 4-11. The Séparately Excited G e n e r a to r ............................ 4-12. The Shunt-Wound Generator ...................................

120 120 120 123 125 128 129 130 131 133 137 139 141

7

Contents

4-13. 4-14. 4-15. 4-16. 4-17. 4-18.

The Compound-Wound G é n é r a t o r ............................ Direct-Current Motors ............................................... The Shunt-Wound M o t o r ........................................... The Séparately Excited Motor ............................... Sériés- and Compound-Wound M o to rs........................ Losses and E ffic ie n c y ...................................................

142 143 145 150 151 153

(lliapter Five. Alternating Current — Basic Concepts and Définitions ..................................................................

155

5-1. Alternating C u rre n t....................................................... 5-2. Génération of a Sinusoidal E M F ............................... 5-3. Phase D ifféren c e........................................................... 5-4. Root-Mean-Square Values of Current andVoltage . . 5- 5. Vector D ia g ra m s .......................................................

155 156 158 160 164

Chapter Six. Single-Phase A. C. C irc u its ...................................

167

6- 1. A General Outline of A. C. C i r c u i t s .................... 6-2. A Circuit Containing Only a R é s is ta n c e .................... (a) Voltage and Current ........................................... (b) Pow er.......................................................................... 6-3. A Circuit Containing Only an In d u c ta n c e ................ (a) Voltage and Current ........................................... (b) Inductive Reactance ........................................... (c) P o w er.......................................................................... (d) The Voltage Across an Inductance as a Fonction of the Magnetic F l u x ........................................... 6-4. A Circuit Containing a Résistance and an Inductance (a) Voltage and Current ........................................... (b) The Impédance of a C i r c u i t ............................... (c) Power .................................................................. 6-5. A Sériés Circuit Containing Résistances and Inductances 6-6. A Parallel Circuit Containing Résistances and Induc­ tances .............................................................................. 6-7. A Circuit Containing Only a C a p a c ita n c e ................ (a) Voltage and Current ........................................... (b) Capacitive Reactance ........................................... (c) Power ...................................................................... 6-8. The Oscillatory C i r c u i t ............................................... 6- 9. Voltage (Sériés) R é s o n a n c e ................................... 6-10. Current (Parallel) Résonance ................................... (a) A Lossless Parallel Résonant Circuit . . . . (b) A Lossy Parallel Résonant C i r c u i t .................... 6-11. The Power Factor ....................................................... 6-12. Active and Reactive E n e r g y ......................................

167 167 167 168 169 169 171 171 173 173 173 175 176 178 180 183 183 184 184 186 188 194 194 196 199 203

Chapter Seven. Three-Phase Networks...........................................

205

7- 1. Three-Phase S y s te m s ............................................... 7-2. A Generator with Star-Connected Windings . . . . 7-3. A Generator with a Delta-Connected Windings . . .

205 207 210

8___________________________________________________ Contents 7-4. Star-Connected L o a d s .................................................. 7- 5. Delta-Gonnected L o a d s ........................................ Chapter Eight. Electrical Measurements and Instruments 8- 1. Basic D é fin itio n s................................................... 8-2. Classification of Electrical Measuring Instruments 8-3. The Movement of an In stru m e n t.............................. (a) The Moving-Coil M ovem ent................................... (b) A Moving-Iron M ovem ent....................................... (c) An Electrodynamic M ovem ent............................... (d) A Ferrodynamic Movement . ................................ 8-4. Measurement of Cuirent andV o lta g e .......................... (a) Moving-Coil Ammeters and V oltm eters................ (b) Rectifier-Type Ammeters and Voltmeters . . . . (c) Thermo-EMF Ammeters and Voltmeters . . . . (d) Moving-Iron Ammeters and Voltmeters . . . . (e) Electrodynamic and Ferrodynamic Ammeters and V o ltm e te rs .............................................................. (f) Digital In s tru m e n ts ............................................... 8-5. Power M easurem ents.................................................. 8-6. Energy Measurement .................................................. 8-7. Résistance M easurem ent.............................................. (a) A Résistance B rid g e ............................................... (b) Measurement of Résistance by the AmmeterVoltmeter M e th o d .................................................. (c) O h m m e te rs .............................................................. (d) Measurement of Insulation R ésistance................ 8- 8. Measurement of Nonelectrical Quantifies by Electrical M e th o d s ......................................................................... (a) Potentiometric T ransducers................................... (b) Induction T ransducers........................................... (c) Thermo-EMF T ra n sd u c e rs ................................... Chapter Nine. Transformera 9- 1. Purpose of Transformera .................................... 9-2. Operating Principle and Design of a Single-Phase Transform er..................................................................... 9-3. Performance of a Single-Phase Transformer at No-Load 9-4. Performance of a Single-Phase Transformer Under Load and the MMF D ia g r a m ....................................... 9-5. Variations in Transformer Voltage at Load . . . 9-6. Power Lost in the Windings of a Loaded Transformer 9-7. The Three-Phase T ra n s fo rm e r.................................. 9-8. Control of Transformer Voltage .................................\ 9-9. A utotransform ers............................................................. \ 9-10. Arc Welding Transformera ...................................... 9-11. Instrument Transformera .......................................... 9-12. Efficiency of a T ra n sfo rm e r...................................... 9-13. Heat Control in T ra n sfo rm era..................................

212 217 223 223 224 228 228 231 232 233 234 235 237 238 239 239 241 242 247 250 250 251 252 254 255 257 258 259 261 261 262 264 267 268 269 270 272 273 \275 276 27§ 27Ù\

9

Contents

Chapter Ten. Alternating-Current Electrical Machines

. . . .

281

10-1. Purpose of Alternating-Current Machines. Induction M o to rs.......................................................................... 281 281 10-2. The Revolving Magnetic F i e l d ......................... 10-3. The Stator Winding of an Induction Motor . . . 284 10-4. The Rotor Winding of an Induction Motor . . . 287 10-5. The Operating Principle of an Induction Motor . 289' 10-6. EMFs in the Stator and Rotor Windings of an Induction M o t o r ...................................................... 291 10-7. The Impédance of the Rotor W i n d i n g ......... 291 10-8. Currents in the Rotor Winding ........................... 293 293 10-9. The Torque of a M o t o r .................................... 10-10. Starting of Induction M o t o r s ......................... 293 298 10-11. Speed Control of an Induction M o t o r ......... 10-12. The Single-Phase Induction M o to r................. 299 10-13. Losses in and Efficiency of an InductionMotor 303 10-14. Synchronous M achines............................................... 304 10- 15. The D.C./A.C. Commutator M o to r.................... 308 Chapter Eleven. Electric Drive and Control Equipment

. . .

11- 1. Electric Drive ....................................................... 11-2. Température Rise of Electrical M a c h in e s ................ 11-3. Sélection of Power Rating for a Motor in Continuous D u t y .............................................................................. 11-4. Sélection of Power Rating for a Motor in ShortTime Duty .................................................................. 11-5. Sélection of Power Rating for a Motor in Intermittent D u t y ............................................................................. 11-6. Knife-Blade Switches ............................................... 11-7. Packet S w itch es.......................................................... 11-8. Starting and Control Rhéostats for Electric Motors 11-9. Control Sw itches........................................................... 11-10. F u s e s .............................................................................. 11-11. Automatic Air Circuit Breakers . . ........................ 11-12. C ontactors...................................................................... 11-13. R elays............................................................................. 11-14. Motor Control Circuits ........................................... 11-15. Control of a Three-Phase Squirrel-Cage Indûction Motor by a Magnetic S t a r t e r ................................... 11-16. Control of a Three-Phase Squirrel-Cage Induction Motor by a Réversible Magnetic S t a r t e r ................ 11-17. Starting of a Two-Speed Squirrel-Cage Induction Motor 11- 18. Automatic Starting of a Three-Phase Slip-Ring Induction M o to r...........................................................

310 310 311 312 313 314 315 317 318 320 322 324 325 326 329 330 331 333 334

Chapter Twelve. Electric Power Transmission and Distribution

337

12- 1. Industrial Distribution Networks .................... 12-2. Industrial Transformer Substations and Switchgear

337 339

Contents

10

12-3. Industrial Power N etw orks.......................................... (a) Overhead and CablePower N e tw o rk s .................. (b) Indoor Wiring ...................................................... (c) Détermination of Conductor Cross-Section on the Basis of Maximum Allowable Température . . . (d) Détermination of Conductor Size on the Basis of Voltage L o s s .......................................................... 12-4. Safety Grounding .....................................................

344 344 348 356

PART TWO. BASIC E L E C T R O N IC S .................................

366

359 361

•Chapter Thirteen. A General Outline of Electronic Processes, Electron Devices .......................................................... 368 13-1. Classification and Use of Electron Devices . . . . 368 13-2. The Motion of Electrons in an Electric Field . . . 369 13-3. The Motion of an Electron in a Uniform Magnetic Field 371 13-4. Electron Emission ...................................................... 373 13-5. Vacuum-Tube Cathodes ........................................ 375 13- 6. The Vacuum D i o d e ......................................... 377 377 (a) Principle of Operation ................... ................... (b) Types of Vacuum Diodes and Their Symbols . . 383 Chapter Fourteen. Vacuum Triodesand Multi-Electrode Tubes 14- 1. The Structure and Principle of Operation of the Vacuum T rio d e .................................................................... 386 14-2. Static Characteristic Curves of the VacuumTriode 14-3. Parameters and Ratings of the Vacuum Triode . . 14-4. Interelectrode Capacitance of the VacuumTriode 14-5. Types of Vacuum T r i o d e s ................................. 398 14-6. Vacuum Tétrodes ...................................................... (a) Principle of Operation ....................................... (b) The Dynatron Effect ........................................... (c) The Beam-Tetrode ............................................... 14-7. Pentodes ...................................................................... 14- 8. Multiple-Unit end Multi-Grid Tubes ................ Chapter Fifteen. Gas-Filled T u b e s ................................

386

388 391 397 399 399 401 402 403 405

407

15- 1. Electric Discharges in Gases and Their Volt-Ampere C h ara cteristics.................................................... 407 15-2. Nonself-Maintaining Arc-Discharge Devices . . . (a) Gas-Filled Thermionic Diodes ........................... (b) Hot-Cathode T h y r a tr o n s ............................ 413 15-3. Glow-Discharge Devices ........................................... (a) Néon Indicator Lamps ....................................... (b) VR Tubes .............................................................. (c) Barretters .............................................................. (d) Glow or Cold-Cathode T h y r a tr o n s ......... 421

411 411 416 416 418 420

11

Contents

15-4. Self-Main taining Arc-Discharge D e v ic e s .................... (a) General ...................................... (b) The E x c itro n .......................................................... (c) The I g n i t r o n .......................................................... 15- 5. Nomenclature for Soviet-Made Gas-Discharge Tubes

423 423 423 427 428

Chapter Sixteen. Semiconductor Devices and Their Application

430

16-1. Intrinsic Conduction in S em iconductors................ 16-2. Impurity or Extrinsic Conduction in Semiconductors 16-3. The Crystal Diode ................................................... 16-4. Germanium and Silicon Diodes ........................... 16-5. Copper-Oxide and Sélénium D io d e s ........................ 16-6. Application of Crystal Rectifiers ........................... 16-7. Marking of Crystal D i o d e s ....................................... 16-8. The Silicon Zener Diode . ....................................... 16-9. Transistors ............................................................... 16- 10. Applicationof Transistors ...................................... (a) Signal A m p lific a tio n ........................................... (b) Configurations of Transistor C i r c u i t s ................ (c) Transistor C h ara c te ristic s................................... 16-11. Type Désignations ofT ra n s is to rs ............................. 16- 12. T hyristors...................................................................

430 432 434 436 439 441 443 444 445 447 447 449 451 454 455

Chapter 1717-2. 17-3. 17-

Seven!een. Photoelectric D e v ic e s ............................. 1. P h o to c e lls ................................................................. The Photomultiplier Tube ...................................... Photoresistors ............................................................. 4. Semiconductor Photovoltaic Cells ......................

460 460 464 465 467

Eighteen. R e c tifie r s ..................................................... 1. Half-Wave R e c tific a tio n ...................................... Full-Wave Rectification .......................................... Three-Phase Rectifiers .............................................. Sélection of Diodes for Rectifier C i r c u i t s ............... Response of an RC Network .................................. (a) Forced Response of an RC N e tw o r k .................... (b) Free Response of an RC N e tw o r k ........................ 18-6. Wave Rectifiers ......................................................... 18- 7. Thyristor R ectifiers..................................................

471 471 475 479 481 482 482 484 486 489

Chapter 1818-2. 18-3. 18-4. 18-5.

Chapter

Nineteen. Audio-Frequency Amplifiers

19- 1. General ..................................................................... A. Transistor A m p lifie rs ........................................... 19-2. Practical Common-Emitter A m p lifie rs .................. 19-3. The Quiescent (Q) Point. Current and Voltage W av efo rm s.......................................... 19-4. Frequency Response of A m plifiers.............................. 19-5. Multistage Transistor A m plifiers.............................. 19-6. The Final Transistor Amplifier Stage ......................

493 493 496 496 499 503 504 506

12

Contents

19-7. Feedback A m p lifie rs .................................................. B. Vacuum-Tube Amplifiers ................................... 19-8. The Basic Vacuum-Triode A.F. Amplifier Stage (a) Am plification.......................................................... (b) Characteristics and Parameters of the Amplifier Stage.......................................................................... (c) Négative Grid B i a s i n g ....................................... (d) Classes of A m p lifie rs ..............................„ . . . 19- 9. Multistage Tube Amplifiers ............................... (a) A Vacuum-Triode Amplifier S t a g e .................... (b) The RC-Coupled Two-Stage Amplifier . . . . 19-10. Power Amplifiers ....................................................... 19-11. Transistors as Switches ........................................... Chapter Twenty. Electronic Oscillators. Oscilloscopes

Chapter Twenty One. Electron-Tube, Solid-State and Photoelectric R e la y s ...................................................................... 21- 1. G e n e ra l..................................................................... 21-2. The D.C. Vacuum-Tube Movable-Contact Relay . . 21-3. The A.C. Vacuum-Tube Movable-Contact Relay . . 21-4. The D.C. 7?C-Network Timing R e l a y ....... 552 21-5. The A.C. i?C-Network Timing R e l a y ....... 553 21-6. The Transistor Timing R e l a y ....................... 554 21-7. The Timing Relay Using a Glow-Discharge Thyratron 21-8. P h o to re la y s ................................................................. 21- 9. The Flip-Flop C irc u it..............................................

2222-2. 22-3. 22-4. 22-5.

• •

512: 516 517 519 519 520 521 526

. . . 528

20- 1. Sinewave or Harmonie O scillators...................... (a) LC O s c illa to rs ....................................................... (b) RC O s c illa to rs ....................................................... 20-2. The Sawtooth VoltageGenerator ................................ 20-3. M u ltiv ib ra to rs............................................................. 20-4. Cathode-Ray T u b e s .................................................. 20-5. The Cathode-Ray O scilloscope.............................. 20- 6. Coding System of Soviet-Made C R T s ......................

Chapter Twenty Two. Fundamentals of Computers

508 509 509 509

528 528 530 532 534 537 548 546548 548 550 551

555 556 558

» . . 562

1. G e n e ra l..................................................................... Structure of a Digital C o m p u te r ........................... Interaction of the Computer U n i t s ....................... The Binary Number System .................................. Arithmetic Operations on Binary Numbers . . . (a) A d d itio n .......................................... (b) S ubtraction.................................................. 568 (c) Multiplication .......................................................... (d) D iv isio n ....................................................... 569 22-6. The Operating Principle of Some Computer Eléments (a) The NOT Gâte ........................................... ........................................... (h) The AND Gâte

562 562 564 565 567 567 569 570 570 571

Contents

(c) The OR Gâte ....................................................... (d) The Diode Network with One Control Input . . . (e) The Shifter .......................................................... 22-7. The Operating Principle of the Binary Counter . . . 22-8. The Operating Principle of the Adder in the Arithmetic Unit .................................................................. 22-9. Delay L i n e s .................................................................. 22-10. Memory Units .......................................................... 22- 11. Input and Output U n i t s .......................................

13

573 574 575 575 577 581 582 587

Chapter Twenty Three. Industrial Applications of Electronics. An Outline of A utom ation........................................... 23- 1. Automatic Systems ................................................... 23-2. Eléments of an Automatic S y s t e m ........................... 23-3. Automatic Inspection and Quality C o n tr o l................ 23-4. Automatic Machine C o n t r o l ....................................... (a) Automatic Drive Control ................................... (b) Time-Sequence Control of Furnace Température (c) Telecontrol on Railways ................................... (d) Numerical Control of M a c h in e s ........................... 23-5. Automatic Process Control ....................................... In d ex .................................................................................................

590 590 590 591 595 595 597 598 603 608 611

B ib lio g ra p h y ..................................................................................

622

Introduction

Electrical engineering has to do with practical applica­ tions of electric energy. This includes electric power géné­ ration, distribution, and conversion. Electric energy has very valuable properties: it can easily be derived from other forms (mechanical, Chemical, etc.), transmitted with low losses for hundreds or even thousands of kilometers to homes and plants, distributed among users and converted back into mechanical, thermal, Chemical, and other necessary forms. Electricity makes it possible to utilize the inexpensive energy accumulated by Nature (energy of falling water), or to eut down its cost (such as when generated by burning peat or low-grade coal). Used on a large scale in ail fields of national economy and everyday life, electricity promotes the introduction of advanced machinery and complex process mechanization and auto­ mation into industry. It has given life to new industrial processes, such as electric welding, electrolysis, and hardening by high-frequency currents. Owing to its abundance and low cost, electricity has provided novel approaches to many problems of industrial production and enabled many breakthroughs in science to become everyday practice and to raise labour productivity. Electronics, which has now become a division of electri­ cal engineering in its own right, considers the principles of operation, design and application of semiconductor, vacuum and gas-filled devices in science, various industries, and technology. For example, semiconductor and gas-filled rectifying devices are used in power engineering to convert alternating current to direct current for electric drives,

16

Introduction

electric traction, electrochemical and other production processes. Without semiconductor, vacuum and gas-filled devices it would be impossible to eïfect process automation, that is, to regulate and control production processes. Rapid advances in computer engineering hâve made it possible not only to raise the performance of automatic control Systems to a new level, but also to tackle nationwide économie problems. Electric and electronic devices for the génération, Pro­ cessing, transmission and display of data are key éléments of automated management and control Systems at any level. Technologies hâve been developed by which a great number of circuit components (diodes, transistors, resistors, capacitors, etc.) can now be made in the form of film micro­ circuits and assembled into sophisticated Systems. In the manufacture of these microcircuits, use is made of electronbeam and laser equipment. Electronics has found uses in the manufacture of superhigh-purity materials, such as tungsten, molybdenum, tantalum and niobium, essential to modem technology. It is obvious that a firm knowledge of the fundamentals of applied sciences, notably electrical engineering and electronics, is essential to any one who wishes to gain insight into present-day technology.

Part One

Electricity

C hapter

Electric

O ne

Field

1-1. General Any body is made up of elementary particles, each carrying an electric charge*. For example, a proton carries a positive charge and an électron, a négative charge. Some charged elementary particles make up atoms and molécules of sub­ stances, others are in the free State. A charged body is one in which positive charge prevails over négative or vice versa; an electrically neutral body has an equal numberof négative and positive charges. Moving elementary particles carrying electric charge, or simply electric charges are inséparable from the surrounding electromagnetic field which is a form of matter. The electromagnetic field consists of two interrelated components, an electric field and a magnetic field. Their existence is revealed by the action they produce on charged elementary particles or bodies. Unlike charges attract and like charges repel one another. Since a charge cannot be isolated from the surrounding mag­ netic field, charged bodies interact via the electric field. As the electric field exerts a force on any electrically char­ ged body or particle placed in it, it is capable of doing work. Therefore, the electric field possesses what is called electric energy. Electrically charged particles of a substance and their electric field are two inseparably linked forms of matter. * Electric charge is a property of material particles or bodies, which characterizes their interaction with their own and an external electromagnetic field. As electric charge is a property of material particles or bodies, it cannot be divorced from matter; yet, when considering electromagnetic effects, it is customary to use “charge” in the sense of charged particles or bodies. In a quantitative définition, charge is synonimous with “quantity of electricity”. 2 -0 2 1 5

Part One. Elecfricity

18

Fig. 1-1. Electric field between two parallel plates carrying dissimilar charges

Any point in an electric field can be characterized in terms of electric field strength, %. Electric field strength is the ratio of the force F that the field exerts on the point test charge Q placed at the point of interest, to this charge, that is* %= F/Q

(1-1)

A point test charge is a charged body very small in size, whose charge is so negligible that it does not practically distort the field being considered. If Q is taken equal to unit y (one coulomb), -

D-c motor

- < s > -

Chemical power source (primary or storage cell) Electric lamp

®

Wire, cable, bus Electric connection, removable and per­ manent connection, removable connection

•

o

Single- and double-pole switches i

R

Fuse Load, resistor

Rhéostat or adjustable resistor

r ^

0

39

Ch. 2. Direct Current Circuits

Table 2-1 (cont.) Circuit Component

Ammeter, voltmeter, wattmeter

Symbol

© © ©

Power sources may be electric (rotary) generators converting mechanical into electric energy, storage or primary cells which convert Chemical energy, etc. Loads include, for example, electric motors which convert electric into mechanical energy, electrolytic cells intended to obtain pure metals (they convert electric into Chemical energy), incandescent lamps and heaters which convert elec­ tric energy into light and heat, etc. In a power source, some form of energy is converted into . electric energy. Due to the work done by external (nonelectric) forces, each unit charge moving in a conductor gains some amount of energy. The amount of energy gained by a unit charge in a conductor is called electromotive force (abbreviated emf). When the external circuit is open-circuited, the emf (designated by the symbol E) is equal to the voltage across the terminais of the power source. Utilizing devices or loads convert electric energy into thërmal, mechanical or Chemical energy. Now the voltage V across the terminais of a load shows how much electric energy is spent per unit charge. The différence between the emf E and the voltage V is the energy that is converted into heat (that is, lost) in moving a unit charge in the power source. It is called the voltage drop (symbolized y 0). So E - V = V0, or E = V + V0 (2-3) Electric power is delivered from power sources to loads by wires. Within short stretch of wire, power loss may sometimes be ignored as has been done above. Wires can be aluminium or copper, insulated or bare. In addition to the three components which hâve been considered, electric circuits usç yayious switçhes, protection

Part One. Electricity

40

devices (fuses and relays), and instruments (such as ammeters, voltmeters, and wattmeters). 2-3. Ohm's Law The ratio of a current I to the cross-sectional area S of a conductor is known as current density (designated by the letter 6): ô = IIS (2-4) Thus, the current density in a conductor is determined by the amount of charge passing through the unit cross-sectional area of the conductor per second, which is proportional to the rate of motion of charged particles along the wire. The rate of motion of the particles is proportional to the field forces, that is, the electric field strength. Thus, the cur­ rent density* in a conductor is proportional to the electric field strength à = yË (2-5) where y = 6/ > A 0 X. As a conséquence, the emf given by Eq. (3-28) is positive and has a clockwise sense. The current due to this emf has the same sense. The magnetic flux produced by this current is in the same direction as the decreasing magnetic flux, which can readily be proved by applying the corkscrew rule. To sum up, a decrease in the flux linking a loop gives rise to an emf and a current such that the résul­ tant magnetic flux tends to oppose the decrease in the flux. If we move the loop of Fig. 3-24 in the opposite direction, the flux linking the loop will build up (AO > 0 ) , so the emf will, according to Eq. (3-28), be négative and hâve a counter-clockwise sense. The magnetic flux it produces will hâve the same sense. The magnetic flux produced by this current will^be opposite to the growing flux due to the loop. To sum up, an increase in the flux due to a loop gives rise to an emf and a current such that the résultant magnetic flux opposes the increase in the flux due to the loop. From the foregoing it follows that the direction of an in­ duced emf is always such that its current opposes the operation (or effect) that has caused it. This law was formulated by H.F.E. Lenz of Russia in 1833. If we increase the current traversing the solenoid of an electromagnet (see Fig. 3-25) or bring doser together a coil and a magnet, the magnetic flux linking the coil will build up, thereby giving rise to an emf and a current, i, in the coil. By Lenz’s law, the direction of the magnetic flux

Part One. Electricity

108

Fig. 3-25. Current duced in a ring

in-

produced by the current i inside the coil is opposite to that of the ïlux due to the electromagnet, so the direction of the induced current can readily be determined by the corkscrew rule. 3-13. Operating Principle of an Electric Generator When a wire is moved (see Fig. 3-26) in the direction of the velocity vector v in a plane perpendicular to the magnetic lines of force, an emf E is induced in the wire. This emf gives rise to a flow of current I around the closed circuit of résistance R . A current-carrying wire, when placed in a magnetic field, is acted upon by an electromagnetic force, F = B II, whose direction, as given by the left-hand rule, is opposite to that[of the velocity vector, so this is a retarding force. Obviously, in order to move a wire one has to apply an external force equal in magnitude and opposite in direction to the retarding force. To State this differently, one needs a prime mover capable of delivering mechanical power P m = Fv, or p m = Fv = BIlv = E l = P Thus, the mechanical energy imparted to the wire to move it through the magnetic field is converted to electric energy, and a wire moved in a magnetic field by some mechanical force may be regarded as an elementary electric generator.

«te

Ch. 3. Elecfromagnetisrh

Fig. 3-26. Operating principle of an electric generator

Recalling Eq. (2-8), the emf of a generator may be written E = V + V0 = IR + Ir0 So, the associated mechanical power P m= E I = I* R + I* r0= VI + P0 = P L + P0 is equal to the electric power P which is the sum of the load power P L = VI and the power lost in the generator, Po = / V 3-14. Operating Principle of an Electric Motor If we place a wire of length^Z inja^uniform field (see Fig. 3-27) so that it is at right angles to the magnetic lines of force, and pass through it a current I supplied by a source of voltage F, the electromagnetic force acting on the wire will, according to Eq. (3-1), be equal to F = BIl and its direction will be that given by the left-hand (wire) rule. This force causes the wire to move with velocity v. In the process, the wire does a mechanical work, and an emf is induced in it. The direction of this emf, as given by the right-hand rule, is opposite to that of the current and its magnitude is E = Bvl If the wire has a résistance r0, then, by Kirchhoff’s voltage law, we may write V - E = Ir0

frart One. Électricity

iiô

Fig. 3-27. Operatingprin­ cip e of an electric motor

or V = E + Ir0 whence the current around the circuit is / = (F — E)/r0

(3-32) (3-33)

Multiplying both sides of Eq. (3-32) by the current I gives the electric power VI = E l + P r0 = BIlv + I 2r0 = Eu + / V0

(3-34)

Here, the product I 2r0 is the power lost as heat in the wires and Eu is the mechanical power. Thus, the electric power generated as a wire is moved through a magnetic field is converted to mechanical power, and this process entails the induction oï a counter-emf. The wire moved through a magnetic field may be regarded as a simple electric motor. Example 3-8. Given: A wire 0.5 m long moved in a magnetic field of 1.2 T induction with a velocity of 20 m/s at right angles to the magnetic lines of force. The résistance of the wire is 0.1 ohm and the terminal (open-circuit) vol­ tage is 15 V. To find: (1) The power in the circuit; (2) the mechanical power developed by the wire; and (3) the power lost as heat. Solution. The counter-emf induced in the wire is E = Blv = 1.2 X 0.5 X 20 = 12 V

Ch. 3. Ëlectromagnetisitt

Vh

The current in the wire is I = (V — E)lr0 = (15 - 12)/0.1 = 30 A The power in the circuit is P = VI = 15 X 30 = 450 W The mechanical power is P m = E l = 12 X 30 - 360 W The power lost as heat is Ph = / 2r0= 302 x 0.1 = 90 W 3-15. Eddy Currents Figure 3-28 shows a métal dise mounted on a pivot and the traces of the pôles of two electromagnets. The magnets produce magnetic ïluxes, and ® 2» which link the dise. Their magnetic induction vectors, B1 and B 2, are shown in the same figure. Any change in the current traversing the coil of one of the electromagnets brings about a change in the magnetic flux with the resuit that eddy currents, ieu are induced in the dise, similar to those induced in a ring-shaped coil (see Fig. 3-25). The direction of the eddy currents can be determined by the same rule as for a coil. The interaction of the eddy currents iel with the magnetic flux ® 2 gives rise to an mmf, Fu which causes the dise to rotate. Figure 3-29 shows the métal dise of a power meter and the trace of a pôle of a permanent magnet. As the dise ro­ tâtes it cuts the magnetic lines of force, and eddy currents ie are induced in the dise. The direction of the emf induced in the dise and of the eddy currents which hâve the same sense is given by the right-hand (coil) rule. The interaction of these currents with the field of the same permanent magnet produces an electromagnetic force and a retarding torque essential for the operation of a power meter. Eddy currents can also be produced by changes in the magnetic fluxes linking the cores (Figs. 3-30a and 3-31a),

112

Fig. 3-28. Eddy currents caused in a dise by variations in a magnetic flux

Part ône. Élêcfficify

Fig. 3-29. Eddy currents induced by rotation of a dise in an unvarying magnetic field

Fig. 3-30. Eddy currents in a steel core

enclosures and other parts of electric machines and apparatus. In such cases, eddy currents not only heat the métal they are flowing in, but also set up magnetic fields of their own, and these fields oppose the operation causing them. Heating by eddy currents constitutes a drain on the primary power source so this conversion of electricity to heat is quite appropriately called eddy-current loss. As a rule, spéci­ fie eddy-current loss is of interest, that is, the loss of power per unit mass of iron, ordinarily expressed in watts per kilogram. Eddy currents can be utilized to advantage in electric furnaces and various heating appliances; but in electric machines and apparatus they entail an additional oss of power and bring down the efficiency.

Ch. 3. Electromagnetism

113

Fig. 3*31. Eddy currents in ^t.he armature of an electric machine

(b)

( a) s o l i d a r m a t u r e ; (b) l a m i nated a rm a tu re

One way to eut down eddy-current loss is to build cores from high-resistance steels, such as those containing 0.5 to 4.8 per cent Silicon (electrical-sheet Steel). Also, the cores of machines should be assembled from thin punchings or laminations (0.1 to 0.5 mm thick), insulated from one another (see Figs. 3-306 and 3-316). 3-16. Inductance. EMF of Self-Induction When a current is flowing around a circuit, each loop or turn of a coil links some amount of magnetic flux. This flux is called the flux of self-induction and symbolized as Ol . The sum of the fluxes of self-induction due to ail turns of a loop or coil is referred to as the flux linkage of self-induc­ tion, WL. If the material has a constant permeability, the magnetic flux and flux linkage of self-induction are proportional to the flux-producing current. The ratio of the flux linkage of self-induction to the lluxproducing current in a loop or coil, witli the permeability of the material held constant, is referred to as the self-in­ ductance (or, simply, inductance) of the loop or coil L = V L/ /

(3-35)

As is seen, the self-inductance of a circuit relates its flux linkage of self-induction to the flux-producing current in the circuit. The SI unit of self-inductance is the henry, H: [L] = [V J /] = Wb/A = V s/A = Qs = H 8 -0 2 1 5

Part One. Elecfricify

114

Fig. 3-32. Diagram sym bol for an inductance

However, the henry is too large to be convenient for practical purposes. Instead, use is made of its submultiples, such as the millihenry, mH (1 mH = 1 X 10"3 H) and the microhenry, pH (1 pH = 1 X 10"6 H). The diagram Symbol for an inductance is shown in Fig. 3-32. Let us détermine the inductance of a ring-shaped coil. The flux linkage of this type of coil is given by Eq. (3-20) V L = w® = iLa (Iw2/l) S and its inductance is L = pa (w2/l) S

(3-36)

As is seen, the inductance of a coil is a function of the coil size, number of turns, and core permeability. Example 3.9. Given: A coil 30 cm (0.3 m) long, 5 cm (0.05 m) in diameter, carrying 2000 turns wound on a nonmagnetic core (pa = p0). To find: The inductance of the coil. Solution. The inductance of a coil is given by Eq. (3-36) L = p0 (w*S/l) = 125 x 10~8 w 22 X 106ji X 52 X 10~4

,

x oo

tj

x ----------Ô3x4-------- = (approx.) 33 mH Any change in the current traversing a circuit (a loop) is accompanied by a change in the magnetic flux and flux linkage of self-induction, which obviously leads to the génération of an emf called the emf of self-induction. The process involved is known as self-induction. The emf of self-induction is, according to Eq. (3-31), given by eL = —dW Jdt or, replacing d*¥L by d (Li), we get = - d V J d t = - d (Li)/dt = - L di/dt

(3-37)

Ch. 3. Electromagnetism

116

Or, in words, the emf of self-induction is proportional to the inductance of the circuit and the rate of change of the fluxproducing current. The direction of the emf of self-induction is given by Lenz’s law. When the flux-producing current is mcreased, that is, when dildt > 0, the emf of self-induction, eL, is négative and, as a conséquence, opposes the flux-producing current. Conversely, when the flux-producing current is reduced, that is, when dildt < 0, the emf of self-induction, eL, is positive and, as a conséquence, aids the flux-produc­ ing current. Example 3-10. Given: A circuit with an inductance of 5 mH, traversed by a current whose rate of change is 600 A/s. To find: The emf of self-induction. Solution. Because the current drops at the rate —dildt = 600 A/s the emf of self-induction is eL= — L dildt = 5 x 10"3 x 600 = 3 V 3-17. Energy of the Magnefic Field When a d.c. source is connected to a circuit having a a résistance and an inductance, the circuit current gradually lises from zéro to its final value given by I = Vlr This rise is accompanied by the build-up of the surrounding magnetic field which stores some of the energy expended by the d.c. source. This energy manifests itself, for example, when the circuit is short-circuited, by maintaining the flow of current until ail of the energy is expended to heat the circuit conductors. It also manifests itself through the interaction of the field with any current-carrying conductor that may be placed in that field. In a coil, the rise of current defined above is accompa­ nied by the génération of the emf of self-induction, eh =

Part One. Êlectriciiy

116

= — L di/dt. By Kirchhoff’s voltage law, we may write V + eL = ir whence V = ir — eL = ir + L di/dt

(3-38)

As is seen, the terminal voltage of the circuit is the sum of two components, ir and L di/dt. The first component is given by Ohm’s law. The second is equal in magnitude but opposite in direction to eL; thus, it balances out the emf of self-induction arising in the circuit. Multiplying both sides of Eq. (3-38) by the product i dt gives Vi dt = i2r dt + Li di The left-hand side of the above équation gives the energy that the circuit receives in the time dt\ the right-hand side of the same équation shows that some of the energy, i2r dt, goes to heat the circuit wire, while the remaining energy, Li di, is stored by the magnetic field round the circuit. If we add together the energy incréments occurring as the circuit current rises from zéro to its final value / , we shall obtain the energy stored by the magnetic field round the circuit / W m = j Li di = L/2/2 = W /2 (3-39) 0 3-18. Mutual Inductance A change in the current flowing around a circuit (in a coil) will induce an emf in another circuit (or coil), if the two are placed in close physical proximity, or coupled, to each other. This process is known as mutual induction. The current I x in the first coil (Fig. 3-33a) gives rise to a magnetic flux part of which, 0 12, links the second coil, w2, thereby producing the flux linkage of mutual induction, T*12 = w2(I)12. The magnetic flux 0 12 and, as a conséquence, the associated flux linkage are proportional to the flux-producing

Ch. 3. Electromagnetism

117

Fig. 3-33. Inductive coupling between two coils

current, I Xl that is ^12

=

M i2/i

whence

(3-40) M1 2 =

The ratio of the flux linkage of one coil to the flux-producing current in the other is called the mutual inductance between the two coils (or circuits). From a comparison of Eqs. (3-35) and (3-40) it follows that the unit of mutual inductance is the same as that of self-inductance — the henry, H. The current / 2 in the second coil (Fig. 3-33b) produces a magnetic flux of its own, 0 2i, which links the turns of the iirst coil, wu thereby producing a flux linkage of mutual inductance, = wx0 2i- As before, the flux linkage and mutual inductance may be written ^

2 1 =

M 21/

2

whence

(3-41) M 21 = ^21^2 Il is an easy matter to show that for two coupled coils or loops M12 = M 21 = M

always, so the subscripts “12” and “21” maysafely bedropped. The mutual inductance between coupled coils is a fonction of the number of turns, size, shape and relative position of the coils, and also the permeability of the medium.

118

Part One. Electricity

A change in the current flowing in one coil brings about a change in the flux linkage of mutual induction, so, by the law of electromagnetic induction (see Sec. 3-12), an emf of mutual induction is induced in the other coil e2 = — cP¥12/dt = — M d ijd t (3-42) Likewise, a change in the current flowing in the other coil brings about a change in the flux linkage of mutual inducti­ on, and emf of mutual induction is induced in the first coil e{ = — dW2l/dt = — M d ijd t (3-43) Or, to State this in words, the emf of mutual induction is proportional to the mutual inductance between the coils and the rate of change of the flux-producing current. The mutual inductance between two coils is connected to the self-inductances of the same coils by a relation of the form M = kY~Lj72 where k is the coefficient of coupling which defines the extent of inductive coupling between two coils. The coefficient of coupling dépends on the relative position of the coils. The shorter the distance between the coils, the greater the coefficient of coupling, and vice versa. Mutual induction is utilized in various machines and apparatus, for example, to transfer energy from one circuit to another or to step up or down a voltage by means of a transformer. Sometimes, mutual induction may be undesirable. For example, if a communication line runs parallel to a power transmission line, the emf of mutual induction induced in the communication circuit may seriously interfère with its operation. 3-19. Magnetohydrodynamic Generator A magnetohydrodynamic (MHD) generator opérâtes on the following principlc. Air, raised in température and enriched with oxygen, is admitted to a combustion chamber where a gaseous fuel is burned to produce a température of about 2500°C. The gaseous

Ch. 3. Elecfromagnetism

119

Fig. 3-34. Sketch of an MHD generator

plasma formed at this température has high electric conductivity. From the combustion chamber, the plasma is admitted at velocity v to an MHD duct, D (Fig. 3-34). Rectangular in cross-section, this duct is formed by two pairs of walls. One pair, E , are the métal électrodes of the MHD generator, and the other pair is made of a dielectric material. External electromagnets set up in the MHD duct a magnetic field of induction 5 , which is at right angles to the longitudinal axis of the duct. When the plasma moves through the magnetic field down the duct (see Fig. 3-34), an electric field is set up in it, which is at right angles to the direction of motion of the plasma and the magnetic field. As a resuit, an emf is induced between the électrodes of the generator, whose magnitude is controlled by the induced electric field I. The power generated by an MHD generator is delivered to load over wires that connect the load to the generator électrodes. In operation under load, forces arise that oppose the motion of the plasma, so an increase in load inevitably slows down the plasma. As we hâve seen, the thermal energy fed to an MHD gene­ rator is first converted to the energy of motion of the plasma, and this is then converted to electric energy. The efficiency of a power plant incorporating an MHD generator may be as high as 60%, which is markedly greater than the efficiency of conventional thermal power plants (43%).

C hapter Four

Direct-Current Electric M achines

4-1. Functions Electric machines are devices intended to convert mechal nical energy to electricity or electricity to mechanical energy. In the former case, they are called electric generators; in the latter, electric motors. Direct-current (d.c.) generators are used to power electric motors, electrolysis cells, battery chargers, and the like. Direct-current (d.c.) motors actuate mechanisms which require large starting torques and speeds adjustable over a wide range, such as electric trains, mine hoists, and rolling mills. In automatic control Systems, d.c. machines can be used as actuators, tachometers, signal converters, etc. In metal-working machine-tools, d.c. machines greatly simplify speed control.

4-2. Design of D.C. Machines A d.c. machine opérâtes on the principles set forth in Secs. 3-13 and 3-14. In sketch form, a two-pole (bipolar) d.c. machine is shown in Fig. 4-1. The machine consists of a steel frame, 7, and a rotating armature, 2. Bolted to the frame are pôles, 3. The pôles (Fig. 4-2) carry a field (exci­ tation) winding (at 4 in Fig. 4-1) having Wf turns and^carrying a field (excitation) current I f. The field winding gives rise to an mmf equal to its ampere-turns I fwf, which in turn sets up an excitation magnetic flux O/, for which the closed path is formed by the pôles, the air gap between the pôles and armature, the armature and the frame (see Fig. 4-1).

Ch. 4. Direct Current Machines

121

Fig. 4-2. Pôle of an electric Fig. 4-3. Armature ol' an electmachine rie machine

The pôles are built up of electrical-sheetj) Steel] laminations and hâve pole-pieces or pole-shoes, 5, whose shape Con­ trols the distribution of the magnetic induction in the air gap Bà. The design of the armature is shown in Fig. 4-3. Its cylindrical body, 7, is assembled from electrical-sheet Steel punchings insulated from one another and press-fitted on a shaft or hub (at 2 in Fig. 4-3a). Slots, 3, in the armature receive the wires (usually called “sides”) of the armature winding (at 4 in Fig. 4-36), which are connected in seriesparallel. The armature winding is insulated from the slots and held in place by suitable wedges or binding wires, 5. The armature shaft also carries a commutator, 6‘, electrically insulated from the shaft. The commutator (Fig. 4-4) is made up of copper commutator segments or bars, 7, in­ sulated from one another] by micanite spacers which are

Part One. Elecfricity

122 Commutator segment J or bar

j

Fig. 4-4. Commutator

Insulation Clamp boit

7 Fig. 4-5. Brushes and a brushholder

Fig. 4-6. External appearance of a d.c. machine

mounted on a sleeve, 2, where they are held in place by bolts. The commutator bars or segments hâve risers, 3, to which the wires of the armature winding are soldered in a definite order. Riding on the commutator surface are stationary carbon or graphite brushes (at 6 in Fig. 4-1) to which are connected leads from an external circuit. In this way, the external circuit is connected via the brushes and commuta­ tor to the rotating armature winding. The arrangement of what is known as brushgear is shown in Fig. 4-5. The prismatic graphite (or graphitized) bru­ shes, i , are held in the brush holders, 2. Each brush holder is mounted on a stud passing through a hole, 4, and supported by, but insulated from, the end shield of the machine. Attached to each brush are flexible copper pig-tails, 3, which connect the brushes to the suitable armature termi­ nais on a terminal board or panel. The terminal panel also carries terminais for the field winding (which may be of the shunt- or the series-wound type) and for the compole (or commutating-pole) winding (see Secs. 4-11 through 4-13). A general view of a d.c. machine is shown in Fig. 4-6.

Ch. 4. Direct Current Machines

123

4-3. Operating Principle of a D.C. Machine A simplified circuit of a d.c. machine is shown in Fig. 47. The brushes are connected to a double-pole (doublethrow) knife-blade switch, 2, so that the armature can be connected to a load r or a supply line. The field winding, 2, is connected to the supply line. Let the armature connected to a load r be actuated by a prime mover, such as a heat engine. Then an emf E will be induced in the armature winding rotating in the field set up by the excitation (field) current // , and a current will be flowing through the load. The direction of the emf and current in the armature 7a, as given by the right-hand rule, is shown in Fig. 4-7. The direction of braking or retarding electromagnetic forces Fb that act on the current-carrying conductors in the magnetic field is likewise marked in the figure. These forces produce a braking (or retarding) tor­ que on the shaft of the machine. The prime mover supplies a torque T which opposes the retarding torque. Thus, as has already been shown in Sec. 3-13, the machine opérâtes as a générât or converting mechanical energy to electricity. By Ohm’s law, the output current is I = I a = El (r + ra) (4-1) So, E = Ir + Ira = V + Ira (4-2) or, stated in words, the generator emf E exceeds the terminal voltage V by the voltage drop across the armature Ira. If we disconnect the shaft of the machine from its prime mover and place the switch in the upward position (see Fig. 4-7) the armature winding will be traversed by a cur­ rent 7 = I a flowing in the direction opposite to that assumed before. The electromagnetic force produced by the inte­ raction of this current with the magnetic field will likewise act in the opposite direction and produce a torque T driving the armature in the previous direction. Now the electric energy coming from the supply line will be converted to mechanical energy (see Sec. 3-14), so the machine will now operate as an electric motor. The commutator and brushes switch the coils in the winding of the rotating armature in such a manuer that

Part One. Electricity

124

Supply line

«I

F----- T.

Fig. 4-7. Explaining the principle of a d.c. machine

each time the active conductors move from the north-pole belt into the south-pole belt the ïlow of current through them is reversed and the machine keeps rotating always in the same direction. As with an electric generator, an emf is induced in the armature winding of the motor. However, this emf opposes the armature current, / a, which can readily be proved by applying the right-hand}*rule. This is called the counter (or back) emf. By Kirchhoff’s voltage law, V — E ~= I ara or

(4-3)

E = V — I ara so the armature current is la = (V - E)/ra

(4-4)

Or, in words, when a machine is operating as a motor, its emf E is less than its terminal voltage V by the voltage drop across the armature winding, Ira. An electric motor can be reversed by reversing the direc­ tion of current flow in the armature or field winding. If the currents in the two^windings are both reversed at the same time, the motor will keep rotating as before (see Fig. 4-7)

Ch. 4. Direct Çurrent Machines

126

4-4. Construction of the Armature Winding 'A simplified circuit of the armature winding is shown in Fig. 4-8. Referring to the figure» there are two pôles» N and 5» between which is rotating an armature with six slots each of which receives two layers of armature coil sides wound with an insulated wire. For simplicity, the slots are not shown in the figure. As is shown in Fig. 4-8, the lead wire starting at commutator bar 1 runs over the near end of the arma­ ture to the top layer of the coil side in the first slot, away from the reader beyond the plane of the drawing, then, as shown by the dashed line, over the far end of the armature to the lower layer of the coil side in the fourth slot whence it is taken over the near end of the armature to the commuta­ tor bar marked 2. The lead wire starting at commutator bar 2 is taken to the upper layer of the coil side in the second slot, and so on. If we trace the run of the winding wire, we shall see that it closes on itself and consists of identical coils, the two ends of each coil being connected to adjacent commutator seg­ ments. This is known as the lap type of winding. When the armature is rotating, an emf is induced in the coil sides enclosed in the slots, so they are called active coil sides. No emf is induced in the wires at the ends of the arma­ ture which are called coil ends. In sketch form a coil of the armature winding is shown in Fig. 4-9. The active sides of the upper layer are represented by a solid line, and that of the lower layer by a dashed line. To give them the desired shape, the coils are wound on suitable formers, then insu­ lated, and dropped in the slots of the armature core. Because each commutator segment receives two leads, namely the finish of the previous coil and the start of the next one, the number of segments K must be equal to that of coils in the armature winding. For the winding shown in Fig. 4-8, the armature has Z = 6 slots and as many coils. Once K is known, it is an easy matter to détermine the number of active conductors that make up the armature winding N = 2wcK where wc is the number of turns per coil.

Part One. Êlectriciïy

126

Fig. 4-8. Arrangement of the armature winding

Fig. 4-9. Armature jwinding [coil

The arrangement of armature windings can conveniently be studied by reference to the drawing in Fig. 4-10. This is the development of the cylindrical surface of the armature and its winding shown in Fig. 4-8. The directions of the emfs induced in the active conductors, as determined by the right-hand rule, are shown in Figs. 4-8 and 4-10. The sum of ail emfs in a closed winding is zéro. However, if we sum the emfs, starting, say, at the first commutator segment and moving in the direction of the emf, we shall notice that at the 4th segment the emf reverses its polarity. This is a junction point, or node, for two parallel branches of the arma­ ture winding, formed relative to the external circuit. As we keep moving down the winding against the emf, we shall run into a second node at commutator segment 2, where the emf reverses its polarity again. Thus, the winding consists of two parallel branches (2a = = 2) with two nodes. The node at the4th commutator segment is the point of the highest potential (+ ), and that atthe first segment, the point of the lowest potential (—). The brushes are positioned to ride on these segments. The voltage between the two brushes at the time corresponding to the po­ sition of the armature shown in Figs. 4-8 and 4-10 is given by yl = e l + e4+^2 + e5 + ^3 + H =

e k ” f" e l

e5 +

e 2 "f" e 6 +

e3

127

Ch. 4. Direct Current Machines

Fig. 4-10. Developed view of an armature winding

Fig. 4-11. Developed an armature winding

view of

where the primed symbols stand for the emfs in the lower layers of the coils. As the armature turns through 60°, the polarity of the brushes and the magnitude of vx remain as they were before, because the sixth slot takes up the position of the first, the first slot takes up the position of the second, and so on. When the armature turns through an angle less than 60°, say, 30°, the winding takes up the position shown in Fig. 4-11, where the brushes, rather than the windings, are shifted to the left for convenience of study. In this position, two coils are short-circuited, and only two coils remain in each of the two parallel branches. At this instant, the machine voltage is v 2 = e l “1“ ^4 + £2 "f £5 = ek + e 'l + e5 + e 2

Thus, as the armature keeps rotating, its terminal voltage remains constant in polarity, but varies from vx to v2 in magnitude. As the number of coils connected in each paral­ lel branch is increased, the ripple in the output voltage is decreased. In present-day machines having a large number of coils, the ripple is so negligible that the output voltage may practically be taken unvarying. The plane passing through the armature axis, that is, within an equal distance of the pôles, and normal to their axis is called the géométrie neutral (Fig. 4-12). The short-circuited coils always move in the géométrie neutral région where the induction B§ is zéro or negligible.

128

Part One. Electricity

Fig. 4-12. Quadrature-axis ar­ mature reaction in a generator

Accordingly, the emf induced in the coils is equal to zéro or negligible. The armature windings of present-day machines are built essentially along the lines discussed above, irrespective of the number of pôles, parallel branches, coils or commutator segments. 4-5. The EMF of fhe Armature Winding As already noted, the emf of a machine is the sum of the emfs of the series-connected conductors in one parallel branch. These emfs are ail different, because the magnetic induc­ tion is different at various points in the air gap around the circumference of the armature. However, the emf of a ma­ chine can be found in terms of the average emf of a conductor multiplied by the number of conductors in one parallel branch. Let the magnetic flux due to one pôle be O; the number of pôles in the machine, 2p\ the axial length of the armature core, Z; its diameter, d\ and its surface area, S. Then the average magnetic induction on the armature surface will be Baü = O x 2 p!S = O x 2plndl (4-5) and the average emf of each conductor will be Eaü = Bavlv = O x 2pn dnlin dl = 0x2

X

60

p (rc/60)

where n is the rotational speed of the armature in révolu­ tions per minute (rpm).

Ch. 4. Direct Current Machines

129

If tlie total number of conductors in the winding is TV, and the number of parallel branches is 2a, then each parallel branch will hâve TV/2a conductors conneGted in sériés. In the circumstances, the emf of a parallel branch and, as a conséquence, that of the machine will be E = Eav (N/2a) = 2p (n/60) (N/2a) (D =c (p/a) (n!60) TV®

(4-6)

or E = cE

(4-23)

drops drastically as the load increases, because O and I (ra + rs) increase both at the same time. This form of response is called a drooping characteristic. At a load less than 25 to 30% P 2ny the motor would run at an excessively high speed because the flux would be very small. This form of duty must be guarded against, because it could cause serious mechanical damage to the motor. A compound-wound motor, that is, one with a sériés- and a shunt-field winding located on the main pôles, behaves partly as a shunt-wound motor and partly as a series-wound motor. The two windings are connected so that their mmfs and, as a conséquence, their respective fluxes, Os/l and Oi